Time Travel without Causal Loops

My thesis is that backwards time travel can occur without causal loops. Specifically, I shall show that assuming that backwards time travel (‘time travel’ for short) is logically possible, it is logically possible to have a world where time travel occurs and yet no causal loops occur. To formulate this thesis more precisely, I need to distinguish two types of causal loops, closed and open causal loops. A causal loop occurs when some event a causes event b, and this event causes event c, and so on, until an event is caused which a cause of a. (There is no restriction on how many events occur in the loop, and whether a set of events counts as forming a causal loop is independent of whether causation is transitive.) A closed loop is one where a is the sole cause of b, b is the sole cause of c, and so on back to a. An open loop, by contrast, is one where, for at least two events in the causal loop f and g, f is one cause of g, but there is another cause of g that is not an event in the loop. In typical time travel stories, the causal loops that occur are open causal loops. For example, in a story where S gets plans for a time travel machine from someone, builds the machine, and then goes back in time to give the plans to S ’s younger self, the plans are involved in a causal loop. But the event of the plans’ being at some particular location in space and time is not the sole cause of the event of the plans’ being at some other location in space and time further in the chain; other events play a role in the plans’ being where they are. The goal of this paper is to show that time travel can occur without open or closed causal loops. I shall give a simple (but contentious) argument for The Philosophical Quarterly  doi: ./j.-...x